Piercing done vertically through the Tongue

Piercing done through the Lip.

Piercing done into the mouth on the left or right side aka Madonna or Monroe 

Piercing done in the center of the upper lip through the Philtrum

Piercing done vertically through the lower lip

Oral piercing groups called bites, including Angle Bites, Snake Bite, Spider Bites, etc...

Piercing done through the upper lip, usually to the side.